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Additions to the MAT 327 web site no longer count towards good deed points
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Week of...
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Notes and Links
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1
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Sep 13
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About This Class, Monday - Continuity and open sets, Thursday - topologies, continuity, bases.
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2
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Sep 20
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Monday - More on bases, Thursdsay - Products, Subspaces, Closed sets, HW1, HW1 Solutions
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3
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Sep 27
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Monday - the Cantor set, closures, Thursday, Class Photo, HW2, HW2 Solutions
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4
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Oct 4
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Monday - the axiom of choice and infinite product spaces, Thursday - the box and the product topologies, metric spaces, HW3, HW3 Solutions
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5
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Oct 11
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Monday is Thanksgiving. Thursday - metric spaces, sequencial closures, various products. Final exam's date announced on Friday.
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6
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Oct 18
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Monday - connectedness in , HW4, HW4 Solutions, Thursday - connectedness, path-connectedness and products
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7
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Oct 25
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Monday - Compactness of , Term Test on Thursday, TT Solutions
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8
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Nov 1
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Monday - compact is closed and bounded, maximal values, HW5, HW5 Solutions, Wednesday was the last date to drop this course, Thursday - compactness of products and in metric spaces, the FIP
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9
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Nov 8
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Monday-Tuesday is Fall Break, Thursday - Tychonoff and a taste of Stone-Cech, HW6, HW6 Solutions
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10
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Nov 15
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Monday - generalized limits, Thursday - Normal spaces and Urysohn's lemma, HW7, HW7 Solutions
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11
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Nov 22
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Monday - and , Thursday - Tietze's theorem
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12
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Nov 29
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Monday - compactness in metric spaces, HW8, HW8 Solutions, Thursday - completeness and compactness
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13
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Dec 6
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Monday - Baire spaces and no-where differentiable functions, Wednesday - Hilbert's 13th problem; also see December 2010 Schedule
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R
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Dec 13
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See December 2010 Schedule
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F
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Dec 20
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Final exam, Monday December 20, 2PM-5PM, at BR200
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Register of Good Deeds
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Add your name / see who's in!
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See Hilbert's 13th
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See some blackboard shots at BBS/10_327-101206-142909.jpg.
Video: Topology-101206
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Dror's notes above / Student's notes below
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Lecture Notes
- Question. The fact that the metric space of real-valued functions on the unit interval with uniform metric is complete uses the fact that [0,1] is compact right? If the function space is defined on a non-compact topological space is that necessarily complete?... -Kai Xwbdsb 00:01, 20 December 2010 (EST)
- No, the compactness of is not used. As we said in class, if is Cauchy in the uniform metric, then for any , the sequence is Cauchy in , so it has a limit. Call that limit ; it is not hard to show that is continuous and that . Theorem 43.6 in Munkres is a slight generalization of this. Drorbn 07:12, 20 December 2010 (EST)
Thanks Dror.
Everybody good luck on the exam!-Kai
Great course! Thank you very much for all your help Dror and all the classmates in this class.
-Kai